1. Field Of The Invention
This invention relates to a temperature constant Gm current reference source.
2. Brief Description Of The Prior Art
In switched capacitor filter design, in order to have well controlled high frequency response, it is desirable to have the gain-bandwidth product of the amplifiers constant. This allows the amplifiers in the filter to settle always in the same amount of time. This is important because such filters are based upon sampling with a set clock period. If the gain-bandwidth product decreases with temperature increase, for example, it takes the amplifiers longer to settle. If the settling time is too long during a clock period, then inaccuracies will develop in the filter. For example, the Q of the filter will degrade, leading to frequency response errors and possible non-linear distortion problems. If the gain-bandwidth product of the amplifier, on the other hand, increases and becomes too large, then, while the signal will settle with sufficient rapidity and AC response will be proper, the total noise in the filter will increase due to the amplifier noise bandwidth increasing, thereby decreasing the signal-to-noise ratio of the system. It is therefore desirable to maintain constant bandwidth.
The common effect between settling and noise in the filter is the gain-bandwidth of the amplifier. The gain-bandwidth of the amplifier is determined by the transconductance (Gm) of the input stage divided by the compensation capacitor. Since the compensation capacitor is temperature stable, then Gm must also be made temperature stable. It is therefore necessary that a temperature stable current reference be provided which stabilizes Gm of a MOSFET over the temperature range to be encountered to the first order.
The equation for the gain-bandwidth (G.B.W.) of an amplifier is the transconductance (Gm) of the input stage thereof divided by the capacitance (C) of the compensation capacitor (G.B.W.=Gm/C). Since the capacitance of the compensation capacitor is independent of temperature, as stated above, it is necessary to stabilize the transconductance (Gm) of the amplifier to achieve the desired result. It is therefore necessary to obtain a current which will stabilize the transconductance of the MOSFET therein. The transconductance of a MOSFET is proportional to the square root of its own mobility term multiplied by the current flowing therethrough where is (Gm=(2uC.sub.o (W/L)I)E0.5), where u is mobility as a function of temperature (u(T)=uo(T/To)E-1.5) where uo is u at To=300 degrees Kelvin and C.sub.o is the oxide capacitance per unit area of the MOSFET, where I=kT ln(N)/qR and where R=R.sub.o [1+TCR(T-300)]. From this relation and with Gm(T) being a constant, a close approximation of the current with TCR=-1667 ppm is I(T)=(KT ln (N))/qRo[1+TCR(T-300)], where K is Boltzmann's constant,N is the ratio of the diodes in one leg of the current mirror to the diode in the other leg thereof and q is the electronic charge. The mobility term has a known physical dependance which operates according to the 3/2 power inverse law. Therefore, a current is required which will operate as a positive 3/2 power so that when the transconductance and current terms are multiplied together there is no temperature dependance.